[Haskell-cafe] deriving instances of Enum for tuples of bounded, enumerable types (useful for generating QuickCheck.Arbitrary instances for collection of collection types)

[Thomas Hartman]

I have some code for creating instances of Enum for a tuple of bounded
enumerable types.

The main win with this was that it makes it easier for me to generate
Test.QuickCheck.Arbitrary instances for types that are based on
collections of enumerable collections -- like you might get when
modeling poker for instance.

In fact, I was trying to answer the question about using QuickCheck
with poker, that Vincent Foley asked a few days ago at

http://groups.google.com/group/fa.haskell/browse_thread/thread/8298c4d838c95505/4e31cc8b859bad24#4e31cc8b859bad24

when I came up with this. (And I am posting a reply to Vincent right
after I finish writing this message.)

Basically I noticed that coming up with the Arbitrary instances seemed
to be tricker than I would have expected. However, it was pretty
straightforward to write an instance of arbitrary for

instance (Enum a, Bounded a) => Arbitrary a where
  arbitrary = do n <- choose (fromEnum (minBound :: a), fromEnum
(maxBound :: a) )
                 return $ toEnum n

So all I needed to do was get my type into instances of Enum and
Bounded, and I got my Arbitrary instance for free. Most of the work
was just writing the instances for various tuples of Bounded
Enumerable types.

Maybe I've been spoiled by how easy many types are gotten using the
magic of the deriving clause, but this seemed like a lot of work to
me. I was wondering if there was an easier way? Or if not, if it would
make sense for something like this to be added to the prelude?

Or is there some sizeable collection of nice Arbitrary instances for
QuickCheck somewheres that I can leverage off of, that hasn't made it
into the standard libraries?

A minor issue: I had a question if I could make the type signatures
for Enum instances less  verbose by doing something like type
BoundedEnum = (Bounded a, Enum a) => a... I tried, and commented out
my attempt as it wouldn't type check. Guidance appreciated.

Thanks, Thomas.

Code follows:


{-# OPTIONS -fglasgow-exts -fallow-undecidable-instances #-}
module EnumInstances where

-- instances of Enum for tuples of types that are both Bounded and Enum

-- typechecks, and does the right thing, though this signature seems
messy, specially when I
-- want to do this kind of thing for longer tuples
instance (Enum a, Enum b,Bounded a, Bounded b) => Enum (a,b)
  where fromEnum (primero,segundo) = ( divFactor * (fromEnum primero)
) + (fromEnum segundo)
          where divFactor = fromEnum (maxBound :: b) + 1
        toEnum i |    (i > (fromEnum (maxBound :: (a,b))))
                   || (i < (fromEnum (minBound :: (a,b)))) = error
"Enum (a,b) bounds error"
                 | otherwise = (a,b)
                     where a = toEnum baseline
                           b = toEnum $ i - (baseline * divFactor )
                           baseline = i `div` divFactor
                           divFactor = (fromEnum (maxBound :: b)) + 1


-- I tried to use a type synonym to write a cleaner type syg but...
type BoundedEnumerable = (Enum a, Bounded a) => a

-- does not typecheck. oh well, the verbose signatures aren't all that bad.
{-
instance Enum (BoundedEnumerable,BoundedEnumerable)
  where fromEnum (primero,segundo) = ( divFactor * (fromEnum primero)
) + (fromEnum segundo)
          where divFactor = fromEnum (maxBound :: b) + 1
        toEnum i |    (i > (fromEnum (maxBound :: (a,b))))
                   || (i < (fromEnum (minBound :: (a,b)))) = error
"Enum (a,b) bounds error"
                 | otherwise = (a,b)
                     where a = toEnum baseline
                           b = toEnum $ i - (baseline * divFactor )
                           baseline = i `div` divFactor
                           divFactor = (fromEnum (maxBound :: b)) + 1
-}




instance (Enum t, Enum t1, Enum t2, Bounded t, Bounded t1, Bounded t2)
=> Enum (t,t1,t2)
  where fromEnum (a,b,c) = fromEnum ((a,b),c)
        toEnum i = (a,b,c)
                     where ((a,b),c) = toEnum i

instance (Enum t, Enum t1, Enum t2, Enum t3, Bounded t, Bounded t1,
Bounded t2, Bounded t3) => Enum (t,t1,t2,t3)
  where fromEnum (a,b,c,d) = fromEnum ((a,b,c),d)
        toEnum i = (a,b,c,d)
                     where ((a,b,c),d) = toEnum i

instance (Enum t, Enum t1, Enum t2, Enum t3, Enum t4,
          Bounded t, Bounded t1, Bounded t2, Bounded t3, Bounded t4)
=> Enum (t,t1,t2,t3,t4)
  where fromEnum (a,b,c,d,e) = fromEnum ((a,b,c,d),e)
        toEnum i = (a,b,c,d,e)
                     where ((a,b,c,d),e) = toEnum i